The present invention relates to a new and distinct strawberry cultivar designated ‘DrisStrawOne’ botanically known as Fragaria×ananassa. This new strawberry cultivar originated from a controlled cross between ‘Driscoll El Capitan’ (U.S. Plant Pat. No. 14,005) and ‘Driscoll Agoura’ (U.S. Plant Pat. No. 15,731). The original seedling of the new cultivar was asexually propagated by stolons at a nursery in Shasta County, Calif. Propagules were transplanted to a controlled breeding plot in Ventura County, Calif. where it was identified and selected for further evaluation in February, 2002. ‘DrisStrawOne’ was subsequently asexually propagated and underwent further testing at various locations in Ventura County, Calif. for four years. The present invention has been found to retain its distinctive characteristics through successive asexual propagations.